26-tone Fokker periodicity block translated to 72-tET

Unison vectors:
1 0 3
3 -1 -3
0 2 -2

Lattice:
25
,'/|\`.
39--/-|-\--9
,'/|\/.60 ,\ |
53--/-|/,'23 `.\|
,'/|\/ 2--\-----44
67 / |/,' `.\| ,'
|\/ 16--------58 \
|/,' \`.\ /,'/ \`.\
30------\--0--/---\-42
\`.\ ,\/|\/. ,\/|
\ 14--/\|/\-56 /\|
,\ |\/.35---------5
28---\|/,'70 `.\|/,'
|\`.49--------19
| ,'12 `.\|/,'
63--------33
`.\|/,'
47

Scale:
0,2,5,9,12,14,16,19,23,25,28,30,33,35,39,42,44,47,49,53,56,58,60,63,67
,70(,72)

Steps:
2,3,4,3,2,2,3,4,2,3,2,3,2,4,3,2,3,2,4,3,2,2,3,4,3,2

Clearly, this one is _begging_ for 5 more notes to become that ME 31-
out-of-72 that Dave discovered. In fact, haven't all our subsets of
72 been subsets of this ME 31-out-of-72? Joseph, would you ever
consider putting 31 notes per octave on your keyboard (with 61 keys,
you'd be just shy of 2 octaves)?

I wrote,

> In fact, haven't all our subsets of
> 72 been subsets of this ME 31-out-of-72?

Well, not all, but quite a few . . .

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_21877.html#21877

This is, without a doubt, one of the MOST "peculiar" lattices I have
yet seen. It looks like a WHOLE BUNCH of hexanies in 3-D??

Isn't that strange.... why is it doing this??

>Joseph, would you ever consider putting 31 notes per octave on your
keyboard (with 61 keys, you'd be just shy of 2 octaves)?

That might work... especially with certain kinds of pieces...

_________ _____ ________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_21877.html#21877
>
> This is, without a doubt, one of the MOST "peculiar" lattices I
have
> yet seen. It looks like a WHOLE BUNCH of hexanies in 3-D??
>
> Isn't that strange.... why is it doing this??

Joseph, you must have missed these lattices when I first posted them
in late February, in their JI form. In 72-tET, you'd probably have
_even more_ hexanies than I'm showing here.

Anyway, the infinite set of 7-limit JI pitches form an infinite 3-D
lattice in which any large portion of the space is divided into equal
numbers of otonal tetrads, utonal tetrads, and hexanies. This is
discussed in my paper, _The Forms Of Tonality_, which you now have.
>
>
> >Joseph, would you ever consider putting 31 notes per octave on
your
> keyboard (with 61 keys, you'd be just shy of 2 octaves)?
>
> That might work... especially with certain kinds of pieces...

The problem with this is that you wouldn't be able to span a 3:2 with
one hand . . . the 3:2 would come out as "an octave and a half" in
normal keyboard terms . . . however, you should be able to play the
hexanies if you use both hands, e.g.:

left right
Keyboard: C-E-G# d-f#-c#'
Rel. Freq.: 8-9-10-11-12-14

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_21877.html#21896

>
> > This is, without a doubt, one of the MOST "peculiar" lattices I
> have yet seen. It looks like a WHOLE BUNCH of hexanies in 3-D??
> >
> > Isn't that strange.... why is it doing this??
>
> Joseph, you must have missed these lattices when I first posted
them in late February, in their JI form. In 72-tET, you'd probably
have _even more_ hexanies than I'm showing here.
>

You're kidding... I don't remember you posting anything about 72-tET
lattices at that time! Well, maybe I missed something... do you have
a reference??

> Anyway, the infinite set of 7-limit JI pitches form an infinite 3-D
> lattice in which any large portion of the space is divided into
equal numbers of otonal tetrads, utonal tetrads, and hexanies. This
is discussed in my paper, _The Forms Of Tonality_, which you now have.

I'm carrying this around with me all the time... I
haven't "digested" it yet, though...

> > >Joseph, would you ever consider putting 31 notes per octave on
> your keyboard (with 61 keys, you'd be just shy of 2 octaves)?
> >
> > That might work... especially with certain kinds of pieces...
>
> The problem with this is that you wouldn't be able to span a 3:2
with one hand . . . the 3:2 would come out as "an octave and a half"
in normal keyboard terms

Oh.... that I DON'T like...

. . . however, you should be able to play the
> hexanies if you use both hands, e.g.:
>
> left right
> Keyboard: C-E-G# d-f#-c#'
> Rel. Freq.: 8-9-10-11-12-14

Ok... that would work...

_______ _____ _____ ____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_21877.html#21896
>
> >
> > > This is, without a doubt, one of the MOST "peculiar" lattices I
> > have yet seen. It looks like a WHOLE BUNCH of hexanies in 3-D??
> > >
> > > Isn't that strange.... why is it doing this??
> >
> > Joseph, you must have missed these lattices when I first posted
> them in late February, in their JI form. In 72-tET, you'd probably
> have _even more_ hexanies than I'm showing here.
> >
>
> You're kidding... I don't remember you posting anything about 72-
tET
> lattices at that time!

I didn't! I repeat . . . I first posted them in late February, in
their JI form.

> Well, maybe I missed something... do you have
> a reference??

Search for a message entitled "What's your favorite number . . ."

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_21877.html#21910

>
> I didn't! I repeat . . . I first posted them in late February, in
> their JI form.
>
> > Well, maybe I missed something... do you have
> > a reference??
>
> Search for a message entitled "What's your favorite number .

Here it is:

/tuning/topicId_19255.html#19255

What incredible shapes! I remember this post, but didn't get
anywhere NEAR the amount out of it as I do now!!

In case anyone wants to do an experiment... after more exposure to
certain things, the perception ENTIRELY changes!

_________ _____ _____ ___
Joseph Pehrson